786 research outputs found
An updated annotated bibliography on arc routing problems
The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to CorberĂĄn and Prins (Networks 56 (2010), 50â69), discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem (GRP) and Arc Routing Problems (ARPs) with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem (CARP) and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising.info:eu-repo/semantics/publishedVersio
Constant-factor approximations for Capacitated Arc Routing without triangle inequality
Given an undirected graph with edge costs and edge demands, the Capacitated
Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity
vehicles so as to satisfy all demands. Constant-factor polynomial-time
approximation algorithms were proposed for CARP with triangle inequality, while
CARP was claimed to be NP-hard to approximate within any constant factor in
general. Correcting this claim, we show that any factor {\alpha} approximation
for CARP with triangle inequality yields a factor {\alpha} approximation for
the general CARP
The two-echelon capacitated vehicle routing problem: models and math-based heuristics
Multiechelon distribution systems are quite common in supply-chain and logistics. They are used by public administrations in their transportation and traffic planning strategies, as well as by companies, to model own distribution systems. In the literature, most of the studies address issues relating to the movement of flows throughout the system from their origins to their final destinations. Another recent trend is to focus on the management of the vehicle fleets required to provide transportation among different echelons. The aim of this paper is twofold. First, it introduces the family of two-echelon vehicle routing problems (VRPs), a term that broadly covers such settings, where the delivery from one or more depots to customers is managed by routing and consolidating freight through intermediate depots. Second, it considers in detail the basic version of two-echelon VRPs, the two-echelon capacitated VRP, which is an extension of the classical VRP in which the delivery is compulsorily delivered through intermediate depots, named satellites. A mathematical model for two-echelon capacitated VRP, some valid inequalities, and two math-heuristics based on the model are presented. Computational results of up to 50 customers and four satellites show the effectiveness of the methods developed
On green routing and scheduling problem
The vehicle routing and scheduling problem has been studied with much
interest within the last four decades. In this paper, some of the existing
literature dealing with routing and scheduling problems with environmental
issues is reviewed, and a description is provided of the problems that have
been investigated and how they are treated using combinatorial optimization
tools
Path Planning for Cooperative Routing of Air-Ground Vehicles
We consider a cooperative vehicle routing problem for surveillance and
reconnaissance missions with communication constraints between the vehicles. We
propose a framework which involves a ground vehicle and an aerial vehicle; the
vehicles travel cooperatively satisfying the communication limits, and visit a
set of targets. We present a mixed integer linear programming (MILP)
formulation and develop a branch-and-cut algorithm to solve the path planning
problem for the ground and air vehicles. The effectiveness of the proposed
approach is corroborated through extensive computational experiments on several
randomly generated instances
A hybrid algorithm combining path scanning and biased random sampling for the Arc Routing Problem
The Arc Routing Problem is a kind of NP-hard routing problems
where the demand is located in some of the arcs connecting nodes
and should be completely served fulfilling certain constraints. This paper
presents a hybrid algorithm which combines a classical heuristic with biased
random sampling, to solve the Capacitated Arc Routing Problem
(CARP). This new algorithm is compared with the classical Path scanning
heuristic, reaching results which outperform it. As discussed in the
paper, the methodology presented is flexible, can be easily parallelised
and it does not require any complex fine-tuning process. Some preliminary
tests show the potential of the proposed approach as well as its
limitationsPostprint (published version
Lower bounds for the mixed capacitated arc routing problem
Capacitated arc routing problems (CARP) arise in distribution or collecting problems where activities are performed by vehicles, with limited capacity, and are continuously distributed along some pre-defined links of a network. The CARP is defined either as an undirected problem or as a directed problem depending on whether the required links are undirected or directed. The mixed capacitated arc routing problem (MCARP) models a more realistic scenario since it considers directed as well as undirected required links in the associated network. We present a compact flow based model for the MCARP. Due to its large number of variables and constraints, we have created an aggregated version of the original model. Although this model is no longer valid, we show that it provides the same linear programming bound than the original model. Different sets of valid inequalities are also derived. The quality of the models is tested on benchmark instances with quite promising results..info:eu-repo/semantics/publishedVersio
Profitable mixed capacitated arc routing and related problems
Mixed Capacitated Arc Routing Problems (MCARP) aim to identify a set of vehicle trips that, starting and ending at a depot node, serve a given number of links, regarding the vehicles capacity, and minimizing a cost function. If both profits and costs on arcs are considered, the Profitable Mixed Capacitated Arc Routing Problem (PMCARP) may be defined. We present compact flow based models for the PMCARP, where two types of services are tackled, mandatory and optional. Adaptations of the models to fit into some other related problems are also proposed. The models are evaluated, according to their bounds quality as well as the CPU times, over large sets of test instances. New instances have been created from benchmark ones in order to solve variants that have been introduced here for the first time. Results show the new models performance within CPLEX and compare, whenever available, the proposed models against other resolution methods.info:eu-repo/semantics/publishedVersio
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